How to select a distribution for parameters?

[rmallen86]

I’m a new user for effective quadratures, and I’m trying to think about how to describe my parameters for a sensitivity analysis. This discourse has a great example case (Sensitivity Analysis with Effective Quadratures) , but I notice that the inputs are all uniform distributions.

Is there any guidance on how to select an appropriate distribution?

I’m planning to perform model runs (the COAWST model) where I have a guess as to “best” model parameter values, but I want to know the impact that the parameter values have on model outputs. For one parameter, I think a reasonable range is [best guess/ 2 to best guess * 2], but it may be that best guess/ 2.1 is also fine. This makes me think that a uniform distribution may not be appropriate, and perhaps gaussian is better? If the answer is “try it a few different ways and look at the impact”, what I should be looking for?

Thank you for the guidance! Feel free to point me towards other answers - I’ve found this discussion which seemed pertinent, but not complete:

Triangular Distribution

There are times in preliminary design when we rarely have enough information about our input data distributions to use anything more involved than either a uniform or triangular distribution (sometimes even the upper and lower bounds of those need to be taken with a pinch of salt!). Nevertheless it’s still valuable to do uncertainty quantification in these early stages as it helps to give an indication of the level of design and development risk which may help inform certain design decisions. T…

[psesh]

Hi @rmallen86, welcome to discourse!

There are a few ways to go about this.

1. If you have data, you can use the data-driven approach, using the data distribution option, as per this link.

2. You can assume a uniform distribution for now, perhaps even with endpoints, and later try to use the Poly instance you generate but with different input distributions. In other words, you would effectively create a surrogate assuming a uniform distribution, and use that surrogate under a different input distribution. This should yield similar results assuming the distributions aren’t wildly distinct.

In terms of what you should be looking for, I would suggest you look at the mean and variance of the Poly instance – to query how they vary under different input distributions.

I would also try to run a couple of test cases within the input domain selected, and query if the Poly's prediction at the test inputs aligns closely with the output of the COAWST model.

Hope this helps.

[rmallen86]

Thanks @psesh , I"ll give this a shot. May take me a little while, but I’ll post back here if I find more questions, or if it goes well and I want to share some results!